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Full text of "Mathematical And Physical Papers - Iii"

ON  THE  COLOUKS  OF  THICK  PLATES.
1C9
mean refrangibility, all the fringes which the overlapping of the different colours allows to be visible are formed inside as well as outside the central white fringe; and if the luminous point be moved still further from the axis, a portion of the field of view around the axis will appear free from rings. If the radius of the central white fringe, or, which is the same, the distance of the luminous point from the axis, be denoted by *JnQ) the radii of the bright fringes of the first, second, ... orders will be denoted, on the same scale, by V(X>  1)> V(wo  2) ... and those of the dark rings by *J(nQ  -J-), \/(??0  f)   
The manner in which the rings open out from the centre as the luminous point is moved sideways out of the axis is very striking, and has been accurately described by Newton. The explanation of it is obvious. It may be remarked that the system of rings, regarded as indefinite, is formed on the same scale whatever be the distance of the luminous point from the axis, but the portion of the indefinite system which alone is visible, in consequence of the coincidence or approximate coincidence of the maxima and minima of intensity corresponding to the several colours, depends altogether upon that distance. Since in passing from the interior to the exterior boundary of a given fringe the square of the radius receives a given increase, it follows that the area of the fringe is constant, that is, independent of the perpendicular distance of the luminous point from the axis. Hence the breadth of the fringe continually decreases as the diameter of the circle which forms cither boundary increases. When a small flame is used for the source of light, and is moved sideways from the axis, the fringes soon become confused, because a flame which does very well for forming the broad fringes of comparatively small radius seen near the axis, will not answer for the fine fringes of large radius which are formed at a distance from the axis. But on using for the source of light the image of the sun in the focus of a small concave mirror belonging to a microscope apparatus, I found that the fringes were formed quite distinctly even when their diameters became very large and consequently their breadths very small.